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Ces\`{a}ro-Orlicz序列空间中的某些重要几何性质
Some Important GeometricProperties inCes\`{a}ro-Orlicz Sequence Spaces

麻振华1,崔云安2
MA Zhenhua1,*, CUI Yunan2,*

1.河北建筑工程学院数理系, 张家口, 河北, 075000; 2.哈尔滨理工大学应用科学学院, 哈尔滨, 黑龙江, 150080
1. Department of Mathematics and Physics, Hebei Institute of Architecture and Civil Engineering,Zhangjiakou, Hebei, 075000, P. R. China;
2. School of Applied Sciences, Harbin University of Science and Technology, Harbin, Heilongjiang, 150080,P. R. C

收稿日期: 2010-11-04
出版日期: 2013-06-25
DOI: 10.11845/sxjz.2010151b

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摘要 }端点是Banach空间中的一个重要的概念,它是研究各种凸性的基础.本文给出了Ces\`{a}ro-Orlicz序列空间中端点的等价条件,以此条件又证明了任何Ces\`{a}ro-Orlicz序列空间都具有$\lambda$-性质,并给出了一致$\lambda$-性质的判定.
关键词 Ces`{a}ro-Orlicz序列空间Luxemburg范数端点$lambda$-性质一致$lambda$-性质    
Abstract:It is known that the extreme pointis very important in Banach space. From the extreme point we can researchmany kinds of convexities. In this paper, necessary and sufficientconditions of extreme point under the Ces\`{a}ro-Orlicz sequencespace $\textrm{ces}_{\phi}$ are presented. It is proved that theCes\`{a}ro-Orlicz sequence space $\textrm{ces}_{\phi}$ equippedwith the Luxemburg norm has the $\lambda$-property. Finally, thecriteria for the uniform $\lambda$-property of the space$\textrm{ces}_{\phi}$ is given.
Key wordsLuxemburgnorm    extreme point    $\lambda$-property    uniform $\lambda$-property
基金资助:Supported by NSFC(No. 10571037)
[1] 吴迪,王士模,燕敦验. \mbox\boldmathn维空间上Hardy算子的加权\mbox\boldmath(L^1, L^q)有界性[J]. 数学进展, 2014, 43(5): 725-732.
[2] 任丽伟;冯国臣;吴从炘;. Kthe-Bochner空间的凸性(英文)[J]. 数学进展, 2006, 35(3): 350-360.
[3] 董浙,鲁世杰. Jacobson子模的端点[J]. 数学进展, 2003, 32(5): 537-546.
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